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  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "from IPython.html.widgets import interact\n",
      "from scipy import  stats\n",
      "import seaborn as sns\n",
      "import pandas as pd"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Previously, we talk about maximum likelihood estimation and maximum a-posteriori estimation and in each case we started out with a probability density function of some kind and we further assumed that the samples were identically distributed and independent. The idea behind robust statistics is to construct estimators that can survive the weakening of either or both of these assumptions.\n",
      "\n",
      "The first idea to consider is the notion of *location*, which is  a generalization of the idea of \"central value\". Typically, we just use an estimate of the mean for this, but we will see shortly why that is a bad idea.  The general idea of Location satisfies the following requirements\n",
      "\n",
      "Let $ X $ be a random variable with distribution $ F $, and let $\\theta(X)$ be some descriptive\n",
      "measure of $F$. Then $\\theta(X)$ is said to be a measure of *location* if for any constants *a* and *b*, we have the following:\n",
      "\n",
      "$$ \\theta(X+b) = \\theta(X) +b $$\n",
      "\n",
      "$$ \\theta(-X) = -\\theta(X)$$\n",
      "\n",
      "$$ X \\ge 0 \\Rightarrow \\theta(X)  \\ge 0 $$\n",
      "\n",
      "$$ \\theta(a X) = a\\theta(X) $$\n",
      "\n",
      "The first condition is called *location equivariance* (or *shift-invariance*  in signal processing lingo). The fourth condition is called *scale equivariance*, which means that the units that $X$ is measured in should not effect the value of the  location estimator.  These Requirements capture the idea of what we intuitively mean by *centrality* of a distribution, or where most of the probability mass is located.\n",
      "\n",
      "For example, the mean estimator is $ \\hat{\\mu}=\\frac{1}{n}\\sum X_i $. The first requirement is obviously satisfied as $ \\hat{\\mu}=\\frac{1}{n}\\sum (X_i+b) = b +  \\frac{1}{n}\\sum X_i =b+\\hat{\\mu}$. Let us consider the second requirement:$ \\hat{\\mu}=\\frac{1}{n}\\sum -X_i = -\\hat{\\mu}$. Finally, the last requirement is satisfied with $ \\hat{\\mu}=\\frac{1}{n}\\sum a X_i =a \\hat{\\mu}$."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "What do we mean by robust estimators?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now that we have the generalized location of centrality embodied in the *location* parameter, what can we do with it?  The next idea is to nail down is the concept of * robust* estimators. Previously, we assumed that our samples were all identically distributed. The key idea is that the samples might be actually coming from a distribution that is contaminated by another nearby distribution, as in the following:\n",
      "\n",
      "$$ F(X) = \\epsilon G(X) + (1-\\epsilon)H(X) $$\n",
      "\n",
      "where $ \\epsilon $ is between zero and one. This means that our data samples $\\lbrace X_i \\rbrace$ actually derived from two separate distributions, $ G(X) $ and $ H(X) $. We just don't know how they are mixed together. What we really want  is an estimator  that captures the location of $ G(X) $ in the face of random intermittent contamination by $ H(X) $. It can get even worse than that because we don't know that there is only one contaminating $H(X)$ distribution out there. There may be a whole family of distributions that are contaminating $G(X)$ that we don't know of. This means that whatever estimators we construct have to be derived from families of distributions instead of a distribution, which is what we have been assuming for maximum-likelihood  estimators. This is what makes robust estimation so difficult --- the extended theory has to deal with spaces of function distributions instead of particular parameters of a particular probability distribution.\n",
      "\n",
      "* Influence function\n",
      "* Outlier Detection\n",
      "* Estimates of location\n",
      "    - definition of location\n",
      "* Trimmed means\n",
      "* Windsorized means\n",
      "* Hodges Lehmann statistics\n",
      "* Asymptotic efficiency\n",
      "* Fisher Consistent\n",
      "\n",
      "* Robust Regression \n",
      "    \n",
      "\n",
      "    - least median\n",
      "    - outliers"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n0=stats.norm(0,1)\n",
      "n1=stats.norm(0,10)\n",
      "xi = linspace(-5,5,100)\n",
      "\n",
      "fig,ax=subplots()\n",
      "ax.plot(xi,n0.pdf(xi))\n",
      "ax.plot(xi,n1.pdf(xi))\n",
      "\n",
      "def bias_coin(phead = .5):\n",
      "    while True:\n",
      "        yield int( np.random.rand() < phead ) \n",
      "\n",
      "pct_mixed  = 0.1\n",
      "bias_coin_gen = bias_coin(pct_mixed)        \n",
      "dual_set = [n0,n1]\n",
      "samples  = [ dual_set[bias_coin_gen.next()].rvs() for i in range(500) ]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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20zIV2rY62ztKPJFiU6xyTetey+0Uq44AcLjjIje1Fd559kJ7T3lF22l5lrMTky+gnwQe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\nIiLiQwpoERERH1JAi4iI+ND/Dwaa89RBQ6jwAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xd7fc910>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "hist(samples,bins=20)\n",
      "title('average = %3.3f, median=%3.3f pct_mixed=%3.3f'%(mean(samples),np.median(samples),pct_mixed))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "<matplotlib.text.Text at 0xd9b6470>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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/7o3AWxaPIjMvi4hnNCxqHJHpp/r+db3MfASg7jBcCnwE+HzDKi3basICOjO/\nCny1cVlE3AW8oz6A7EJ1xn4k1fXDITOBhyaqXiVq1lYNr70iqrOZy4H96OK2GqmdIuJ5wDeB92fm\nDXXP0HZq7WG6uJ1GMbxdDOfRNbZND+5DG0TEHOAyYGFmfjMiPtvwcsu22qJD3Jm5Z2YekpmHAL8F\nDsvMNcBARDyzHgI/DLh+1IK6QER8KCLeUj99BFhnW/2piNiH6uz0mMy8CiAzH8Z2asl2GpG3LN48\nSyJibv34CNyHAIiInYGrgdMz8+J68Wa11VaZxV1rnLn2buAbwLbAVZl5y9apUlG+ClwSEcdTtcvQ\nbVNtq019kmr29nn1ZZOHMvP12E4jGcTvXivesrg9Q/vR+4ELI2IqcDuweOtVqSjzqYawz4yIoWvR\n86iOVW21lbf6lCSpQN6oRJKkAhnQkiQVyICWJKlABrQkSQUyoCVJKpABLUlSgQxoSZIKZEBLklSg\n/w/AANf0JyzowwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xd7f4dd0>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import sympy.stats\n",
      "from sympy.abc import x\n",
      "eps = sympy.symbols('epsilon')\n",
      "\n",
      "mixed_cdf = sympy.stats.cdf(sympy.stats.Normal('x',0,1),'x')(x)*(1-eps) + eps*sympy.stats.cdf(sympy.stats.Normal('x',1,2),'x')(x)\n",
      "mixed_pdf = sympy.diff(mixed_cdf,x)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plot_mixed_dist(epsilon=.1):\n",
      "    n1 = stats.norm(1,2)\n",
      "    xi = linspace(-5,5,100)\n",
      "    fig,ax = subplots()\n",
      "    ax.plot(xi,[sympy.lambdify(x,mixed_pdf.subs(eps,epsilon))(i) for i in xi],label='mixed',lw=2)\n",
      "    ax.plot(xi,n0.pdf(xi),label='g(x)',linestyle='--')\n",
      "    ax.plot(xi,n1.pdf(xi),label='h(x)',linestyle='--')\n",
      "    ax.legend(loc=0)\n",
      "    ax.set_title('epsilon = %2.2f'%(epsilon))\n",
      "    ax.vlines(0,0,.4,linestyle='-',color='g')\n",
      "    ax.vlines(epsilon,0,.4,linestyle='-',color='b')\n",
      "\n",
      "interact(plot_mixed_dist,epsilon=(0,1,.05))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "<function __main__.plot_mixed_dist>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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z2kwhrCaDt4QIIT39IzS1DRAbY2NhYZrV4QTM8hLPzcbOmlYqu2voGen1UUII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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x112c4810>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "M-estimators"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "M-estimators are generalized maximum likelihood estimators. Recall that for maximum likelihood, we want to maximize the likelihood function as in the following:\n",
      "\n",
      "$$ L_{\\mu}(x_i) = \\prod f_0(x_i-\\mu)$$\n",
      "\n",
      "and then to find the estimator $\\hat{\\mu}$ so that\n",
      "\n",
      "$$ \\hat{\\mu} = \\arg \\max_{\\mu} L_{\\mu}(x_i) $$\n",
      "\n",
      "So far, everything is the same as our usual maximum-likelihood  derivation except for the fact that we don't know $f_0$, the distribution of the $\\lbrace X_i\\rbrace$. Making the convenient definition of\n",
      "\n",
      "$$ \\rho = -\\log f_0 $$\n",
      "\n",
      "we obtain the more convenient form of the likelihood product and the optimal $\\hat{\\mu}$ as\n",
      "\n",
      "$$ \\hat{\\mu} = \\arg \\min_{\\mu} \\sum \\rho(x_i-\\mu)$$\n",
      "\n",
      "If $\\rho$ is differentiable, then differentiating  this with respect to $\\mu$ gives\n",
      "\n",
      "$$ \\sum \\psi(x_i-\\hat{\\mu}) = 0 $$\n",
      "\n",
      "with $\\psi = \\rho'$ and for technical reasons we will assume that $\\psi$ is increasing. The key idea here is we want to consider general $\\rho$ functions that my not be MLE for *any* distribution.\n"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "The distribution of  M-estimates "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For a given distribution $F$, we define $\\mu_0=\\mu(F)$ as the solution to the following \n",
      "\n",
      "$$ \\mathbb{E}_F(\\psi(x-\\mu_0))= 0 $$\n",
      "\n",
      "It is technical to show, but it turns out that $\\hat{\\mu} \\sim \\mathcal{N}(\\mu_0,\\frac{v}{n})$ with\n",
      "\n",
      "$$ v = \\frac{\\mathbb{E}_F(\\psi(x-\\mu_0)^2)}{(\\mathbb{E}_F(\\psi^\\prime(x-\\mu_0)))^2} $$\n",
      "\n",
      "Thus, we can say that $\\hat{\\mu}$ is asymptotically normal with asymptotic value $\\mu_0$ and asymptotic variance $v$. This leads to the efficiency ratio which is defined as  the following:\n",
      "\n",
      "$$ \\texttt{Eff}(\\hat{\\mu})= \\frac{v_0}{v} $$\n",
      "\n",
      "where $v_0$ is the asymptotic variance of the MLE and measures how near $\\hat{\\mu}$ is to the optimum. for example, if for two estimates with asymptotic variances $v_1$ and $v_2$, we have $v_1=3v_2$, then first estimate requires three times as many observations to obtain the same variance as the second.\n",
      "\n",
      "For example, for the sample mean (i.e. $\\hat{\\mu}=\\frac{1}{n} \\sum X_i$) with $F=\\mathcal{N}$, we have $\\rho=x^2/2$ and $\\psi=x$ and also $\\psi'=1$. Thus, we have $v=\\mathbb{V}(x)$. Alternatively, using the sample median as the estimator for the location, we have $v=\\frac{1}{4 f(\\mu_0)^2}$. Thus, if we have $F=\\mathcal{N}(0,1)$, for the sample median, we obtain $v=\\frac{2\\pi}{4} \\approx 1.571$. This means that the sample median takes approximately 1.6 times as many samples to obtain the same variance for the location as the sample mean."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "One way to think about M-estimates is a weighted means. Most of the time, we have $\\psi(0)=0$ and $\\psi'(0)$ exists so that $\\psi$ is approximately linear at the origin. Using the following definition:\n",
      "\n",
      "\n",
      "$$ W(x)  =  \\begin{cases}\n",
      "                \\psi(x)/x & \\text{if} \\: x \\neq 0 \\\\\n",
      "                \\psi'(x)  & \\text{if} \\: x =0 \n",
      "            \\end{cases}\n",
      "$$\n",
      "\n",
      "We can write our earlier equation as follows:\n",
      "\n",
      "$$ \\sum W(x_i-\\hat{\\mu})(x_i-\\hat{\\mu}) = 0 $$\n",
      "\n",
      "Solving this for $\\hat{\\mu} $ yields the following,\n",
      "\n",
      "$$ \\hat{\\mu} = \\frac{\\sum w_{i} x_i}{\\sum w_{i}} $$\n",
      "\n",
      "where $w_{i}=W(x_i-\\hat{\\mu})$. The question that remains is how to pick the $\\psi$ functions."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Huber functions"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The family of Huber function is defined by the following:\n",
      "\n",
      "$$ \\rho_k(x ) = \\begin{cases}\n",
      "                x^2  & \\text{if} \\: |x|\\le k \\\\\n",
      "                2 k |x|-k^2 & \\text{if} \\: |x| \\gt k\n",
      "                \\end{cases}\n",
      "$$\n",
      "\n",
      "with corresponding derivatives $2\\psi_k(x)$ with\n",
      "\n",
      "$$ \\psi_k(x ) = \\begin{cases}\n",
      "                x  & \\text{if} \\: |x|\\le k \\\\\n",
      "                \\text{sgn}(x)k & \\text{if} \\: |x| \\gt k\n",
      "                \\end{cases}\n",
      "$$\n",
      "where the limiting cases $k \\rightarrow \\infty$ and $k \\rightarrow 0$ correspond to the mean and median, respectively. To see this, take $\\psi_{\\infty} = x$ and therefore $W(x) = 1$ and thus the defining equation results in\n",
      "\n",
      "$$ \\sum_{i=1}^{n} (x_i-\\hat{\\mu}) = 0 $$\n",
      "\n",
      "and then solving this leads to $\\hat{\\mu} = \\frac{1}{n}\\sum x_i$. Note that choosing $k=0$ leads to  the sample median, but that is not so straightforward to solve for."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig,ax=subplots()\n",
      "colors=['b','r']\n",
      "for k in [1,2]:\n",
      "    ax.plot(xi,np.ma.masked_array(xi,abs(xi)>k),color=colors[k-1])\n",
      "    ax.plot(xi,np.ma.masked_array(np.sign(xi)*k,abs(xi)<k),color=colors[k-1],label='k=%d'%k)\n",
      "ax.axis(ymax=2.3,ymin=-2.3)\n",
      "ax.set_ylabel(r'$\\psi(x)$',fontsize=28)\n",
      "ax.set_xlabel(r'$x$',fontsize=24)\n",
      "ax.legend(loc='best')\n",
      "ax.set_title('Huber functions')\n",
      "ax.grid()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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U0pEkrYZueypBUml47vu/Y/O213ho8KmWAqlIOTGQ1Cl1z89nk+G70ZLqwQdP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\n/w/1WiHm90hy1AAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x11447d90>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The $W$ function corresponding to Huber's $\\psi$ is the following:\n",
      "\n",
      "$$ W_k(x) = \\min\\Big{\\lbrace} 1, \\frac{k}{|x|} \\Big{\\rbrace} $$\n",
      "\n",
      "which is plotted in the following cell for a few values of $k$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig,ax=subplots()\n",
      "ax.plot(xi,np.vstack([np.ones(xi.shape),2/abs(xi)]).min(axis=0),label='k=2')\n",
      "ax.plot(xi,np.vstack([np.ones(xi.shape),1/abs(xi)]).min(axis=0),label='k=1')\n",
      "ax.axis(ymax=1.1)\n",
      "ax.legend(loc=0)\n",
      "ax.set_title(\"Huber's weight function\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "<matplotlib.text.Text at 0x117bf510>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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MTiLMRIqxCCqP18cH+xqIdjlYNjvd6DgTIntSm0ugZWzVnbgCFs5KJSEmgo/2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\nuuzqnWYL8Nwyd1/fQCBfLyT1XDnLlvbtNPd8it1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       "text": [
        "<matplotlib.figure.Figure at 0xd7f4cb0>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Another alternative intuitive way  to interpret  the M-estimate is to rewrite the following:\n",
      "\n",
      "$$ \\hat{\\mu} = \\hat{\\mu} +\\frac{1}{n}\\sum_i \\psi(x_i-\\hat{\\mu}) = \\frac{1}{n} \\sum_i \\zeta(x_i,\\hat{\\mu})$$\n",
      "\n",
      "which for the Huber family of functions takes on the form :\n",
      "\n",
      "$$ \\zeta(x,\\mu) = \\begin{cases}\n",
      "                    \\mu - k & \\text{if} \\: x \\lt \\mu-k \\\\\n",
      "                    x & \\text{if} \\: \\mu-k \\le x \\le \\mu+k \\\\\n",
      "                    \\mu+k & \\text{if} \\: x \\gt \\mu \\\\\n",
      "                  \\end{cases}\n",
      "$$\n",
      "\n",
      "Thus, the interpretation here is that $\\hat{\\mu}$ is the average of the truncated pseudo-observations $\\zeta_i$ where the observations beyond a certain point are clipped at the $k$-offset of the $\\hat{\\mu}$. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Asymptotic variance"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sympy import mpmath, symbols, diff, Piecewise, sign, lambdify\n",
      "from sympy.stats import density, cdf, Normal\n",
      "from sympy.abc import k,x"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "eps = symbols('epsilon')\n",
      "lpdf=diff(cdf(Normal('x',0,1))(x)*(1-eps)+ eps*cdf(Normal('x',0,10))(x),x)\n",
      "p = Piecewise((x,abs(x)<k),(k*sign(x),True))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def closure_on_asymptotic_variance(mn=(0,0),std=(1,10)):\n",
      "    from sympy.abc import k,x\n",
      "    eps = symbols('epsilon')\n",
      "    lpdf=diff(cdf(Normal('x',mn[0],std[0]))(x)*(1-eps)+ eps*cdf(Normal('x',mn[1],std[1]))(x),x)\n",
      "    def asymptotic_variance(kval,epsval):\n",
      "        p = Piecewise((x,abs(x)<kval),(kval*sign(x),True))\n",
      "        denom=mpmath.quad(lambdify(x,lpdf.subs(eps,epsval)),[-kval,kval])**2\n",
      "        numer=mpmath.quad(lambdify(x,(p.subs(k,kval))**2*lpdf.subs(eps,epsval)),[-np.inf,np.inf])\n",
      "        return float(numer/denom)\n",
      "    return asymptotic_variance"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "case2=closure_on_asymptotic_variance()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "kvals= [.001,0.3,0.5,.7,1.00001,1.4,1.7,2,3,4,5]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig2,ax=subplots()\n",
      "ax.plot(kvals,[case2(k,0) for k in kvals],'-o',label='eps=0')\n",
      "ax.plot(kvals,[case2(k,.05) for k in kvals],'-o',label='eps=.05')\n",
      "ax.plot(kvals,[case2(k,.1) for k in kvals],'-o',label='eps=0.1')\n",
      "ax.set_xlabel(\"k\")\n",
      "ax.set_ylabel(\"asymptotic variance\")\n",
      "ax.legend(loc=0)\n",
      "ax.set_title(r\"$\\mathcal{N}(0,1) , \\mathcal{N}(0,10)$ mixed\",fontsize=18)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "<matplotlib.text.Text at 0x114e2b30>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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HVqdoVUpdDPyotd6IOXnLZqXUuZZHJoQQIuCqf97F7gf+TP6rL2MLDyfjyqvp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\nYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1189df30>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Computable Example"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nsamples = 500\n",
      "ncols = 300\n",
      "xs = np.array([dual_set[bias_coin_gen.next()].rvs() for i in range(ncols)*nsamples ]).reshape(nsamples,-1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig,ax=subplots()\n",
      "ax.hist(np.mean(xs,0),20,alpha=0.8,label = 'mean')\n",
      "ax.hist(np.median(xs,0),20,alpha=0.3,label ='median')\n",
      "ax.legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "<matplotlib.legend.Legend at 0xd8b60b0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x11368af0>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig,ax=subplots()\n",
      "sns.violinplot(np.vstack([np.median(xs,axis=0),np.mean(xs,axis=0)]).T,ax=ax,names=['median','mean']);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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7eG57V7XFjrWgH7aiAVicxfIhlKG0eIiYbwsJ3xaS0QAWq43x4ycy/fCZDB8+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\nSdIAMZglSRogBrMkSQPEYJYkaYD8F6LuDuqcYvtYAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x11621e50>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def huber_estim(x,k=1,tol=1e-6):\n",
      "    if x.ndim==2: # loop over columns\n",
      "        out = []        \n",
      "        for i in range(x.shape[1]):\n",
      "            out.append(huber_estim(x[:,i],k=k)) # recurse        \n",
      "        return np.array(out)\n",
      "    else:\n",
      "        mu = median(x)\n",
      "        mad = median(abs(x-mu))*1.4826 # follow MADN convention\n",
      "        while True:\n",
      "            mu_i=mean(minimum(maximum(mu-k*mad,x),mu+k*mad))\n",
      "            if abs(mu-mu_i) < tol*mad: break\n",
      "            mu = mu_i\n",
      "        return mu_i"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "huber_est={k:huber_estim(xs,k) for k in [1,1.5,2,3]}\n",
      "huber_est[0] = np.median(xs,axis=0)\n",
      "huber_est[4] = np.mean(xs,axis=0)\n",
      "fig,ax=subplots()\n",
      "sns.violinplot(pd.DataFrame(huber_est),ax=ax)\n",
      "ax.set_xticklabels(['median','1','1.5','2','3','mean']);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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08UdoaWrCdn46knz2e13WuWnIeh333v/XhL5gGejoURePP/owWXoDF1rO3v04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\nXckFF16Mt/EgnUfPrNE6sJrWRHwc8rt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Lc3PLAlXoLUePPkKRr4hToeCsn3M6FCTuODz6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\nTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x11b81030>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "huber_est={k:huber_estim(xs,k) for k in kvals}\n",
      "huber_est_df = pd.DataFrame(huber_est)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig,ax=subplots()\n",
      "sns.violinplot(huber_est_df,ax=ax)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 20,
       "text": [
        "<matplotlib.axes._subplots.AxesSubplot at 0x11d1b0f0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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b6SgZ+4RXViyBq/c2bHosC3Y+2e5h9hpuYrHS58ELEuasF/wbLzz9JOfnisVn01nhkzGf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\nBeZEIpFIJJqIFJgTiUQikWgi/gHqTqICuvZjhAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x113bfd30>"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig2,ax=subplots()\n",
      "ax.plot(kvals,[case2(k,pct_mixed) for k in kvals],'-o',label='eps=0.1')\n",
      "(huber_est_df.var()*nsamples).plot(marker='o',label='est eps=0.1',ax=ax)\n",
      "ax.set_xlabel(\"k\")\n",
      "ax.set_ylabel(\"asymptotic variance\")\n",
      "ax.legend(loc=0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 21,
       "text": [
        "<matplotlib.legend.Legend at 0x11d84ef0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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8HctruFPIrVrrZ5RSAcAeYBGwFvidqcmEEEIAvt2Vvi+3ildXH6Kh2U7mwBi+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\nmV2G02UQEWJj6lV9mTwqmbDgnjeDnOz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       "text": [
        "<matplotlib.figure.Figure at 0x1175c270>"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "References"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "* Maronna, R. A., R. D. Martin, and V. J. Yohai. \"Robust Statistics: Theory and Methods\". 2006."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}